Question

In 2006, 95% of new cars in the US came with a spare tire. In 2017, 72% came with a spare tire.

Answer 1

Using the Central Limit Theorem, it is found that:

• The mean is 0.23.

• The standard deviation is $s = \sqrt{\frac{0.95(0.05)}{250} + \frac{0.72(0.28)}{250}}$.

Central Limit Theorem

• It states that for a proportion p in a sample of size n, the sampling distribution of sample proportions has mean $p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$

• When two variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

In 2006, 95% of new cars in the US came with a spare tire, with a sample of 250, hence:

$p_1 = 0.95, s_1 = \sqrt{\frac{0.95(0.05)}{250}}$

In 2017, 72% of new cars in the US came with a spare tire, with a sample of 250, hence:

$p_2 = 0.72, s_2 = \sqrt{\frac{0.72(0.28)}{250}}$

Hence, for the distribution of differences:

$p = p_1 - p_2 = 0.95 - 0.72 = 0.23$

$s = \sqrt{s_1^2 + s_2^2} = \sqrt{\frac{0.95(0.05)}{250} + \frac{0.72(0.28)}{250}}$

To learn more about the Central Limit Theorem, you can take a look at brainly.com/question/16695444